{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from statsmodels.api import tsa\n",
    "from dateutil.parser import parse\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "def parse_quarter(string):\n",
    "    \"\"\"\n",
    "    Converts a string from the format YYYYQN in datetime object at the end of quarter N.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Note: you could also just retrieve the first four elements of the string\n",
    "    # and the last one... Regex is fun but often not necessary\n",
    "    year, qn = re.search(r'^(20[0-9][0-9])(Q[1-4])$', string).group(1, 2)\n",
    "    \n",
    "    # year and qn will be strings, pd.datetime expects integers.\n",
    "    year = int(year)\n",
    "    \n",
    "    date = None\n",
    "    \n",
    "    if qn=='Q1':\n",
    "        date = pd.datetime(year, 3, 31)\n",
    "    elif qn=='Q2':\n",
    "        date = pd.datetime(year, 6, 30)\n",
    "    elif qn=='Q3':\n",
    "        date = pd.datetime(year, 9, 20)\n",
    "    else:\n",
    "        date = pd.datetime(year, 12, 31)\n",
    "        \n",
    "    return date\n",
    "\n",
    "\n",
    "alcohol_consumption = pd.read_csv('data/NZAlcoholConsumption.csv', \n",
    "                                  parse_dates=['DATE'], \n",
    "                                  date_parser=parse_quarter,\n",
    "                                  index_col='DATE')\n",
    "alcohol_consumption.sort_index(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "wine = alcohol_consumption.TotalWine\n",
    "wine_diff = wine.diff(4).dropna()\n",
    "time_series = wine_diff\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ARMA model\n",
    "\n",
    "AR models a point in the time series as a linear model of the previous values. The mismatch $e_t$ is assumed to be \"noise\".\n",
    "However there could still be information in the series of $e_t$! How about we add the past errors as additionnal features?\n",
    "\n",
    "This leads to the **ARMA** model with an autoregressive part that you will recognise and a part that corresponds to a moving average:\n",
    "\n",
    "$$\n",
    "y_{t} = c + \\underbrace{ \\phi_{1}y_{t-1} + \\phi_{2}y_{t-2} + \\dots + \\phi_{p}y_{t-p} }_{AR(p)} + \\underbrace{ \\theta_{1}e_{t-1} + \\theta_{2}e_{t-2} + \\dots + \\theta_{q}e_{t-q} }_{MA(q)} +e_{t},\n",
    "$$\n",
    "\n",
    "ARMA models are also implemented in `statsmodels` and their implementation is consistent with the one of AR models. \n",
    "\n",
    "* Create an ARMA model with `tsa.ARMA`, specify $p=3$ and $q=3$\n",
    "* Fit and predict\n",
    "* Display\n",
    "\n",
    "Since the result will look almost identical to just using AR, you will want to show the MAE as well. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/envs/cspark/lib/python3.6/site-packages/statsmodels/tsa/base/tsa_model.py:225: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
      "  ' ignored when e.g. forecasting.', ValueWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "arma = tsa.ARMA(time_series, order=(3, 3))\n",
    "arma_result = arma.fit()\n",
    "prediction = arma_result.predict(start=3)\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "plt.plot(time_series, '-o', label='true')\n",
    "plt.plot(prediction, '-o', label='model')\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE = 0.127\n"
     ]
    }
   ],
   "source": [
    "print('MAE = {0:.3f}'.format(mean_absolute_error(time_series[3:], prediction)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
